Method and apparatus for judging deformation of vertebral body

ABSTRACT

A method for judging deformation of a vertebral body includes the steps of measuring a central length (a), rear brim length (c), and front brim length (d) from a profile X-ray image of a vertebral body to be judged, determining ratios of c/d, a/c and a/d, and classifying deformation of the vertebral body to be judged by using indices, c, d, c/d, a/c and a/d. Furthermore, a method for judging deformation of a vertebral body, which comprises obtaining at least two indices by measuring a central length (a), vertebral body width (b), rear brim length (c), and front brim length (d) from a profile X-ray image of a vertebral body, analyzing these indices by a discriminant function, and classifying a deformation of the vertebral body from results of the analysis.

This is a continuation of application Ser. No. 07/541,173 filed Jun. 20,1990, which is a continuation of application Ser. No. 07/046,751 filedMay 7, 1987, both now abandoned.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method and apparatus for judgingdeformation of a vertebral body. More particularly, the presentinvention relates to a method and apparatus for judging deformation of avertebral body which is one of the bones forming the spinal column. Ajudgment of the presence of vertebral body deformation accompanied byosteoporosis, as well as a classification of the deformation, is veryimportant for grasping the progress of osteoporosis and for confirmationof the effect of therapy.

2. Description of the Related Art

In the prior art, the presence of deformation of a vertebral body whichis one of the bones forming the spinal column has been judged by aphysician by visual observation of the profile X-ray images of thoracicvertebrae or lumbar vertebrae. However, compared with a fracture of theso called long bones such as the femur, tibia, radius, ulna, etc., ajudgment of vertebral deformation is difficult since this is usually awedge-shaped deformation, pressure fracture, depressed fracture, etc.,and any judgment inevitably involves individual differences. Also, evenif an attempt is made to monitor changes over a period of time, forconfirmation of the effect of therapy, because the deformation cannot bequantified, progress of the deformation, if any, cannot be easilydetermined.

Also, although a method has been reported in which the ratio (a/d) ofthe central length (a) to the front brim length (d) of the third lumbarvertebrae is determined as the index (Lumbar Spine Score) for the degreeof bone atrophy, or a change in the longitudinal and lateral bone beamsof the third lumbar vertebrae is observed as the index for the degree ofbone atrophy (severity classified by Jikei University), or a judgment ofthe fracture of a vertebral body is made by measurement of the centrallength (a), front brim length (d) and rear brim length (c) of avertebral body The New England Journal of Medicine, vol. 306, 446 (Feb.25, 1982), a method for classifying the type of deformation of avertebral body has not heretofore been known.

SUMMARY OF THE INVENTION

Accordingly, the objects of the present invention are to eliminate theabove-mentioned disadvantages of the prior art and to provide a methodfor objectively judging deformation of a vertebral body.

Other objects and advantages of the present invention will be apparentfrom the following description.

In accordance with the present invention, there is provided a method forjudging deformation of a vertebral body, which comprises measuring acentral length (a), a rear brim length (c), and front brim length (d)from a profile X-ray image of a vertebral body to be judged, determiningratios of c/d, a/c, and a/d, and classifying deformation of thevertebral body to be judged by using indices, c, d, c/d, a/c and a/d.

In accordance with the present invention, there is also provided amethod for judging deformation of a vertebral body, which comprisesobtaining at least two indices by measuring a central length (a),vertebral body width (b), rear brim length (c), and front brim length(a) from a profile X-ray image of a vertebral body, analyzing theseindices by discriminant function and classifying a deformation of thevertebral body from results of said analysis.

In accordance with the present invention, there is further provided anapparatus for judging deformation of a vertebral body comprising (i) aninput means for inputting at least two values of a central length (a),vertebral body width (b), rear brim length (c), and front brim length(d) from a profile X-ray image of a vertebral body to be judged, (ii) anarithmetic means for operating the calculation necessary fordiscriminating "wedge-shaped vertebrae", "inverse wedge-shapedvertebrae", "fish vertebrae", and "no deformation" to at least two typesby using the above-mentioned input value, (iii) a means fordiscriminating the at least two types by using the calculation results,(iv) a means for inputting the discriminant function and/or standardnecessary for the calculation and discrimination, and (v) an outputmeans for outputting the judgment result.

BRIEF DESCRIPTION OF THE DRAWING

The present invention will be better understood from the description setforth below with reference to the accompanying drawings, in which:

FIG. 1 shows a profile X-ray image of a vertebral body;

FIG. 2 shows the relationships of the respective vertebral bodydeformations and front brim length (d), rear brim length (c), etc.,according to the judgment method of the present invention;

FIG. 3 shows an example of vertebral body deformation;

FIG. 4 shows the front brim length, central length, rear brim length,and vertebral body width in a profile X-ray image of a vertebral body;

FIG. 5 is a block diagram illustrating the basic structure of anapparatus for judging deformation of a vertebral body by using an X-rayimage of the vertebral body;

FIG. 6 is a block diagram illustrating an apparatus for judgingdeformation of a vertebral body in the X-ray image of the vertebral bodyto be judged by using a discriminating standard obtained mainly fromX-ray images of vertebral bodies having no substantial deformation, inwhich a means for inputting information relating to X-ray images ofvertebral bodies having deformation caused therein is further required;

FIG. 7 is a block diagram illustrating an apparatus for judgingdeformation of a vertebral body by using, as a criteria, adiscriminating standard obtained by mainly using a discriminatingfunction;

FIG. 8 shows an apparatus for judging deformation of a vertebral bodycomprising a digitizer for inputting the points 1 to 6 in FIG. 1 or thepoints 1 to 8 in FIG. 4 from the X-ray image to a computer; a personalcomputor for classifying the presence or absent of the deformation andtypes of the deformation by measuring the lengths a, c, and d in FIG. 1or a, b, c, and d in FIG. 4, followed by the image treatment; a memoryincluding a software for effecting the above-mentioned treatment; and aprinter for printing out, for example, the measured values or the typesof deformation; and

FIG. 9 shows an apparatus for judging deformation of a vertebral bodycomprising a TV camera for reading the image of each vertebral body fromthe X-ray image; a personal computer for classifying the presence orabsence of the deformation and the types of the deformation by measuringthe lengths a, c, and d in FIG. 1 or the lengths a, b, c, and d in FIG.4 from the read X-ray image; a including a software for registering theabove images and effecting the above-mentioned treatment.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The present inventors have made an intensive study of a method ofobjective evaluation of vertebral body deformation, and found that thepresence of a vertebral body deformation can be objectively judged usinga standard in which lengths of the vertebral body and their ratios arecombined by accurately measuring the lengths of a front brim, rear brim,central portion from a profile X-ray image (i.e., an image on a filmtaken from the side by X-ray radiation) of a vertebral body anddetermining the ratios of the respective portions of the vertebral body.The present inventors names and further found that the type of vertebralbody deformation can be judged according to the standard lengths of thevertebral body and their ratios are, and the progress over a period oftime of the vertebral body deformation can be judged from the change inthe deformation type as well as a change in the lengths of the vertebralbody. In view of the above findings, the inventors accomplished thepresent invention.

In the prior art, the profile X-ray image of vertebral body was visuallyobserved by a physician in order to determine vertebral bodydeformation, but according to the present invention, the lengths of therespective portions of the vertebral body are measured, judgmentstandards are prepared with reference to a judgment by a physician, andthe presence of vertebral body deformation as well as a classificationof the deformation type are objectively performed following the judgmentstandards.

The judgment method of the present invention is now described in moredetail.

(i) First, from a profile X-ray of a vertebral body without deformation,the central length (a), rear brim length (c), and front brim length (d)of each vertebral body are measured to determine an average value (c) ofc, an average value (d) of d, and a standard deviation (σ_(c), σ_(d)).

The above measurement is used to obtain standard values which become thejudgment standard for the central length (a), rear brim length (c), andfront brim length (d), etc., determined from a patient whose vertebralbody deformation is to be judged.

The vertebral body without deformation to be measured is preferably avertebral body of a person of from 50 to 75 years old, in view of theage of the patient whose vertebral body deformation is to be judged.Also, it is preferable to perform measurements separately for men andwomen, and it is desirable to perform measurements of about 50 vertebralbodies, or more, for both men and women.

When making a profile X-ray image of a vertebral body, the thoracicvertebrae from the first thoracic vertebrae to the twelfth thoracicvertebrae, lumbar vertebrae from the first lumbar vertebrae to the fifthlumbar vertebrae should be included, giving a total of 17 vertebralbodies, and therefore, for example, it is advantageous to take thephotograph of the profile X-ray image with the eighth thoracic vertebraeas the center separately from the profile X-ray image with the thirdlumbar vertebrae as the center. In the profile X-ray image with theeighth thoracic vertebrae as the center, the first thoracic vertebraecannot be accurately measured in most cases, and further, the second andthe third thoracic vertebrae are unclear in many cases. However, sincethe frequency of vertebral body deformation is not great in thesevertebral bodies, it is sufficient if measurement can be made from thefourth thoracic vertebrae or the fifth thoracic vertebrae.

The center length (a), rear brim length (c), and front brim length (d)of a vertebral body are specifically as shown in FIG. 1. Fordetermination of these values, for the profile X-ray image of avertebral body, the central length (a), rear brim length (c), and frontbrim length (d) may be measured for each vertebral body with a scale orslide calipers, but the six points of 1 to 6 shown in FIG. 1 can beinput through a digitizer into a computer to measure the central length(a) (3-4), rear brim length (c) (5-6), and front brim length (d) (1-2),and to calculate the ratios of c/d, a/c, a/d. Also, for example, thedegree of blackening may be recorded with a TV camera, etc., and thelengths of the respective portions of the vertebral body may beautomatically measured by image processing.

(ii) Subsequently, from the profile X-ray image of the vertebral body ofthe patient whose vertebral body deformation is to be judged, as in (i),the center length (a), rear brim length (c), and front brim length (d)of each vertebral body are measured, and further, the ratios of c/d, a/cand a/d are determined by calculation.

These measurements can be conducted exactly as in the case of the above(i).

(iii) Next, a judgment of vertebral body deformation can be made from a,c, d, c/d, a/c and a/d, for example, as follows.

That is, (A) when c/d, c, d, a/c, a/d satisfy the following conditions,the judgment can be "no deformation" (type N):

(a) 0.7<c/d<1.4;

(b) at least one of c≧c-2σ and d≧d-1.5σ_(d) is satisfied; and

(c) at least one of a/c>0.8 and a/d>0.8 is satisfied.

As the judgment standard for such "no deformation", the ratio c/d of therear brim length to the front brim length must be between 0.7 and 1.4 asthe first condition (a). For, as described below, if c/d becomes 1.4 ormore, the front brim portion becomes a deformed wedge-shaped vertebrae,and if c/d becomes 0.7 or less, the rear brim portion becomes a deformedinverse wedge-shaped vertebrae, which in practice is very rare.

Next, as the second condition (b), at least one of rear brim length cand front brim length d must be greater than c-2σ_(c) and d-1.5σ_(d)when the average values of the rear brim length c and front brim lengthd of vertebral body without deformation determined in (i) are made c andd, respectively. In a typical healthy vertebral body, a, c, d all have ahigh value, namely a≧a-2σ_(a), c≧c-2σ_(c), d≧d-1.5σ_(d), but even whenthe vertebral body is slightly compressed to become a≧a-2σ_(a), providedthat at least one of the conditions of c≧c-2σ_(c) or d≧d-1.5σ_(d), canbe satisfied, no clear vertebral body deformation is recognized andjudgment of "no deformation" may be made.

As the third condition, at least one of a/c and a/d must be more than0.8. For, if both of a/c and a/d are 0.8 or less, namely the centerlength a is much smaller, than the rear brim length c and front brimlength d, a fish vertebrae condition as described below is determined.

Thus, for the above reasons, when the above conditions of (a), (b) and(c) are satisfied, a judgment of "no deformation" can be made.

The relationship of the conditions of (a), (b), and (c), or therespective conditions as described below with the respective types ofvertebral body deformation, including "no deformation", are shown inFIG. 2.

(B) When c/d≧1.4, the judgment can be a "wedge-shaped vertebrae" (typeI).

In the wedge-shaped vertebrae, deformation has occurred at the frontbrim portion as shown in FIG. 3, and the front brim length (d) hasbecome much smaller than the rear brim length (c). For example, when thefront brim length is 3/4 of the rear brim length (c/d=1.33), awedge-shaped vertebral body deformation can be easily recognized, but insome cases, a clear wedge-shaped vertebrae cannot be easily recognized.On the other hand, when the front brim length is 2/3 of the rear brimlength (c/d=1.5), it can be clearly recognized as a wedge-shapedvertebrae, and therefore, c/d≧1.4 is made the judgment standard forwedge-shaped vertebrae.

In addition to the so called wedge-shaped vertebrae, the wedge-shapedvertebrae (type I) is inclusive of deformations with shortened frontbrim length, like a wedge-shaped vertebrae, as a result of, for example,an upper brim pressure fracture, upper brim depressed fracture, lowerbrim pressure fracture, lower brim depressed fracture, and as describedbelow, even in the case of a vertebral body which is judged as a flatvertebrae because a<a-2σ_(a), c<c-2σ_(c), d<d-1.5σ_(d), if there is aremarkable deformation at the front brim portion satisfying c/d≧1.4, itcan be judged to be a wedge-shaped vertebrae.

(C) When c/d≦0.7, the judgment can be an "inverse wedge-shapedvertebrae" (type IV).

The inverse wedge-shaped vertebrae may be defined as a vertebral bodywherein deformation has occurred at the rear brim portion, and thus therear brim length (c) has become smaller than the front brim length (d),contrary to the wedge-shaped vertebrae wherein deformation has occurredat the front brim portion, and the front length (d) has become smallerthan the rear brim length (c) (see FIG. 3), but in practice, such avertebral body does not substantially exist. In the fifth lumbarvertebrae, as shown in Example 1, the rear brim length (c) is smallerthan the front brim length (d), with the average value of c/d beinglower than 1, e.g., 0.95, but in some cases, an inverse wedge-shapedvertebrae cannot be clearly recognized even when the rear brim length(c) is 3/4 of the front brim length (d) (c/d=0.75), and therefore, ajudgment of an inverse wedge-shaped vertebrae (type IV) can be made whenc/d≦0.7.

(D) When c, d, c/d satisfy the conditions shown below, the judgment canbe a "flat vertebrae" (type III):

(a) c<c-2σ_(c) ;

(b) d<d-1.5π_(d) ; and

(c) 0.7<c/d<1.4.

In the first condition (a) and the second condition (b), the rear brimlength (c) and the front brim length (d) are both smaller than c-2σ_(c)and d-1.5σ_(d) when the average values of the vertebral body withoutdeformation are made c and d; namely, c<c-2σ_(c) and d<d-1.5σ_(d).

The flat vertebrae is a vertebral body having a relatively uniformdeformation at the front brim portion, the central portion, and the rearbrim portion under pressure (see FIG. 3); namely, all of the front brimlength (d), the central length (a) and the rear brim length (c) aresmaller. As shown by the average values of the lengths of the respectiveportions of the vertebral body without deformation of Example 1, sincethe central length (a) is smaller than the front brim length (d) or therear brim length (c) even in the vertebral body without deformation, thespecific feature of the flat vertebrae resides in a particularly smallfront brim length (d) and rear brim length (c), and the vertebral bodywherein c<c-2σ_(c) and d<d-1.5σ_(d) is judged to be a flat vertebrae(type III). The conditions of -2σ_(c) for C and -1.5σ_(d) for D are setbecause c is greater than d (c>d) as shown in Example 1, and thus C andD become approximately equal values by setting such conditions, tosatisfy the conditions for a flat vertebrae. The third condition (c) is0.7<c/d<1.4. For, even where a<a-2σ_(a), c<c-2σ_(c), d<d-1.5σ_(d),deformation at the front brim portion is particularly marked, and wherec/d≧1.4, it can be judged to be a wedge-shaped vertebrae, while in thecase of a marked deformation at the rear brim portion when c/d≦0.7, itis judged to be an inverse wedge-shaped vertebrae.

(E) When c/d, c, d, a/c, a/d satisfy the following conditions, thejudgment can be a "fish vertebrae" (type II):

(a) 0.7<c/d<1.4;

(b) at least one of c≧c-2σ_(c) and d≧d-1.5σ_(d) is satisfied;

(c) a/c≦0.8 and a/d≦0.8.

"Fish vertebrae" is a vertebrae where a depressed fracture or a pressurefracture has occurred at the central portion, whereby the central length(a) is particularly smaller than the front brim length (d) and rear brimlength (c) (see FIG. 3). Accordingly, among the so called "nodeformation" classifications, except for wedge-shaped vertebrae, flatvertebrae, and inverse wedge-shaped vertebrae, the central length (a) isparticularly smaller. When the central length (a) is smaller than thefront brim length (d) and the rear brim length (c), thus satisfyinga/c<0.9 and a/d<0.9, deformation such as fish vertebrae can be clearlyrecognized, but in some cases a clear fish vertebrae cannot berecognized, and therefore, a/c<0.8 and a/c<0.8 can be made the judgmentstandards for fish vertebrae.

In addition to the so called fish vertebrae, the fish vertebrae (typeII) is also inclusive of deformations with a shortened central lengthlike fish vertebrae, as a result of an upper brim pressure fracture,upper brim depressed fracture, lower brim pressure fracture, lower brimdepressed fracture, etc.

The relationships between these judgment standards for "no deformation","wedge-shaped vertebrae", "inverse wedge-shaped vertebrae", "flatvertebrae" and "fish vertebrae", are shown in FIG. 2.

In the judgment as described above, explanation has been made byselecting the upper limit as 1.4 and the lower limit as 0.7 as thejudgment standard for c/d as a preferable example, but these values canbe selected freely, for example, in the case of the upper limit, fromthe range of 1.25 to 1.55, preferably from 1.33 to 1.5, more preferablyfrom 1.4 to 1.45. The lower limit can be selected freely from the rangeof 0.8 to 0.6, preferably from 0.75 to 0.65.

As the judgment standard for a/c and a/d, 0.8 was selected in the caseof "no deformation" and "fish vertebrae", but this value can be freelyselected from the range of 0.65 to 0.9, preferably from 0.7 to 0.85,more preferably from 0.75 to 0.8.

As the judgment standard for c and d, c-2σ_(c) and d-1.5σ_(d) wereselected in the case of "no deformation", "flat vertebrae", and "fishvertebrae" but the judgment standard for c can be freely selected fromthe range of c-1.0σ_(c) to c-2.5σ_(c), preferably c-1.25σ_(c) toc-2.25σ_(c), more preferably c-1.5σ_(c) to c-2.0σ_(c). The judgmentstandard for d also can be similarly selected from the range ofd-1.0σ_(d) to d-2.5σ_(d), preferably d-1.25σ_(d) to d-2.25σ_(d), morepreferably d-1.5σ_(d) to d-2.0σ_(d).

As mentioned above, although the coefficients β₁ to β₆ can be previouslyset in the present invention, β₁ to β₆ may optionally be determined froma discriminating function capable of discriminating two groups with twovariants or two groups with one variant by using values obtained bymeasuring two of a, b, c and d, with respect to at least five profileX-ray image in each of two types among four types (i.e., wedge-shapedvertabrae, fish vertabrae flat vertebral, and no deformation). Astypical examples, β₁ is z₅ obtained by the following discriminantfunction using the ratio c/d derived from c and d, which are obtained bymeasuring at least five profile X-ray images in each of two typesselected from "wedge-shaped vertebrae" and "no deformation":

(i) When the standard deviation σ₁ of c/d of at least five profile X-rayimage of "wedge-type vertebrae" is substantially the same as thestandard deviation σ₂ of c/d of at least five profile X-ray images of"no deformation". ##EQU1## wherein μ₁ and μ₂ are averages of c/drelating to the profile X-ray images of "wedge-shaped vertebrae" and "nodeformation", respectively, π₁ and π₂ are numbers of the X-ray images of"wedge-type vertebrae" and "no deformation", respectively, μ is anaverage of μ₁ and μ₂, and σ is an average of σ₁ and σ₂ ; and

(ii) When σ₁ and σ₂ are substantially different, ##EQU2## wherein μ₁ andμ₂ are averages of c/d relating to the profile X-ray images of"wedge-shaped vertebrae" and "no deformation", respectively, π₁ and π₂are the number of the X-ray images of "wedge-type vertebrae" and "nodeformation", respectively.

Furthermore, the present inventors have made an intensive study of amethod of objective evaluation of vertebral body deformation, and foundthat the presence of a vertebral body deformation as well as thedeformation type can be judged objectively by use of a discriminantfunction by accurately measuring the lengths of, for example, the frontbrim (d), rear brim (c), central portion (a), and the vertebral bodywidth (b) from a profile X-ray image of a vertebral body, and furtherfound that the progress over a period of time of the vertebral bodydeformation can be judged from the change in the type of saiddeformation as well as the change in the lengths of the vertebral body,and thus accomplished the present invention.

In the prior art, vertebral body deformation has been judged by aphysician by visual observation of the profile X-ray image of avertebral body, but according to the method of the present invention,the lengths of the respective portions of a vertebral body are measuredand for the vertebral bodies judged by a physician to be "nodeformation", "wedge-shaped vertebrae", "fish vertebrae", and "flatvertebrae", discrimination is made by discriminant functions todetermine discriminant formulae for the respective types of vertebralbody deformations, and thereafter, the presence of vertebral bodydeformation and the type of deformation are objectively judged by thesediscriminant formulae for a patient whose vertebral body deformation isto be judged.

The types of deformed vertebral bodies are classified in the presentinvention generally into wedge-shaped vertebrae, fish vertebrae, andflat vertebrae.

In the wedge-shaped vertebrae (type I), deformation has occurred at thefront brim portion as shown in FIG. 4, and the front brim length hasbecome particularly smaller than the rear brim length, including inaddition to the so called wedge-shaped vertebrae deformation with ashortened front brim length like wedge-shaped vertebrae as the result ofupper brim pressure fracture, an upper brim depressed fracture, lowerbrim pressure fracture, and lower brim depressed fracture, etc. In thefish vertebrae (type II), the depressed fracture or pressure fracturehas occurred at the central portion, whereby the central length hasbecome particularly smaller than the front brim length and rear brimlength (see FIG. 4), including in addition to the so called fishvertebrae deformations with a shortened center length like fishvertebrae as the result of upper brim pressure fracture, an upper brimdepressed fracture, lower brim pressure fracture, and lower brimdepressed fracture, etc.

In the flat vertebrae (type III), the front brim portion, centralportion, and rear brim portion are deformed relatively uniformly underpressure (see FIG. 4); namely, all of the front rear length, centrallength, and rear brim length are smaller.

In addition, there is the inverse wedge-shaped vertebrae (type IV). Thistype is defined as a vertebral body wherein deformation has occurred atthe rear brim portion, and thus the rear brim length is smaller than thefront brim length, contrary to the wedge-shaped vertebrae wheredeformation has occurred at the front brim portion, and the front brimportion is smaller than the rear brim length (see FIG. 4). In practice,however, such a vertebrae does not substantially exist. Accordingly, itis sufficient if the four types, wedge-shaped vertebrae, fish vertebrae,flat vertebrae and "no deformation", can be classified.

The judgment method of the second aspect of the present invention is nowdescribed in more detail.

(i) First, the vertebral body, central length (a), vertebral body width(b), rear brim length (c), and front brim length (d) of each of thevertebrae judged by a physician as "no deformation", wedge-shapedvertebrae, fish vertebrae and flat vertebrae, are measured from aprofile X-ray of the vertebral body.

The above measurement is used to determine the discriminant formula fordiscriminating the presence of vertebral body deformation as well as thedeformation type. Accordingly, the vertebral bodies of these respectivetypes should be preferably vertebral bodies of persons generally 50 to75 years old, in view of the age of the patient whose vertebral bodydeformation is to be judged. Also, it is preferable to performmeasurements separately for men and women, and it is desirable toperform measurements of about fifty or more vertebral bodies for bothmen and women. However, since wedge-shaped, vertebrae, fish vertebraeand flat vertebrae do not widely occur, the discriminant formula fordiscrimination of the vertebral body deformation type according to themethod of the present invention can be determined if at least five eachof these deformed vertebral bodies can be measured.

Also, from the first to twelfth thoracic vertebrae and the first to thefifth lumbar vertebrae, the size differs for each vertebral body, andtherefore, it is necessary to measure each vertebral body and determineeach deformation type.

When making a profile X-ray image of a vertebral body, the thoracicvertebrae from the first thoracic vertebrae to the twelfth thoracicvertebrae, lumbar vertebrae from the first lumbar vertebrae to the fifthlumbar vertebrae should be included, giving a total of seventeenvertebral bodies, and therefore, for example, it is advantageous to takethe photograph of the profile X-ray image with the eighth thoracicvertebrae as the center separately from the profile X-ray image with thethird lumbar vertebrae as the center. In the profile X-ray image withthe eighth thoracic vertebrae as the center, the first thoracicvertebrae cannot be accurately measured in most cases, and further, thesecond and the third thoracic vertebrae are unclear in many cases.However, since the frequency of vertebral body deformation is not greatin these vertebral bodies, it is sufficient if measurement can be madefrom the fourth thoracic vertebrae or the fifth thoracic vertebrae.

The center length (a), width (b), rear brim length (c), and front brimlength (d) of a vertebral body are specifically as shown in FIG. 4. Fordetermination of these values, from the profile X-ray image of avertebral body, the central length (a), width (b), rear brim length (c),and front brim length (d) may be measured for each vertebral body with ascale or slide calipers, but the eight points of 1 to 8 shown in FIG. 4can be input through a digitizer into a computer to measure the centrallength (a) (3-4), width (b) (7-8), rear brim length (c) (5-6), and frontbrim length (d) (1-2). Also, for example, the degree of blackening maybe recorded with a TV camera, etc., and the lengths of the respectiveportions of the vertebral body may be automatically measured by imageprocessing.

(ii) Next, discriminant formula for discriminating "no deformation",wedge-shaped vertebrae, fish vertebrae, and flat vertebrae isdetermined. Such a discriminating analysis is described in, for example,Chuichi Okuno et al "Multivariate Analytical Method" (published byNikkagiren); Chuichi Okuno et al "Overall Multivariate AnalyticalMethod" (published by Nikkagiren); Koichi Sugiyama "Introduction toMultivariate Data Analysis" (published by Asakura Shoten), and others,and calculation can be made by referring to these sublications. However,by inputting the central length (a), vertebral body width (b), rear brimlength (c), and front brim length (d) of the respective deformationtypes determined in (i) by a commercially available computer program(e.g., BMD multivariate analysis program from IBM Co.), the discriminantformula for discriminating "no deformation", wedge-shaped vertebrae,fish vertebrae, and flat vertebrae can be simply obtained. Suchdiscriment formulae are specifically described as follows. That is, thefollowing formulae and the vertebral body is judged from the maximumvalue of z₁ to z₄ :

    z.sub.1 =a.sub.10 +a.sub.11 x.sub.1 +a.sub.12 x.sub.2 +a.sub.13 x.sub.3 +a.sub.14 x.sub.4

    z.sub.2 =a.sub.20 +a.sub.21 x.sub.1 +a.sub.22 x.sub.2 +a.sub.23 x.sub.3 +a.sub.24 x.sub.4

    z.sub.3 =a.sub.30 +a.sub.31 x.sub.1 +a.sub.32 x.sub.2 +a.sub.33 x.sub.3 +a.sub.34 x.sub.4

    z.sub.4 =a.sub.40 +a.sub.41 x.sub.1 +a.sub.42 x.sub.2 +a.sub.43 x.sub.3 +a.sub.44 x.sub.4

wherein z₁, z₂, z₃, and z₄ are discriminant values of "wedge-shapedvertebrae", "fish vertebrae", "flat vertebrae", and "no deformation",respectively, x₁, x₂, x₃, and x₄ are variables corresponding to acentral length, vertebral body width, rear brim length, and front brimlength, respectively, a₁₀, a₂₀, a₃₀, and a₄₀ are constants, and a₁₁ toa₄₄ are coefficients. This discriminant formula must be determined foreach vertebral body from the first thoracic vertebrae to the fifthlumbar vertebrae, generally from the fourth thoracic vertebrae to thefifth lumbar vertebrae. (iii) Next, from the profile X-ray image of thevertebral body of the patient whose vertebral body deformation is to bejudged, the central length (a), vertebral body width (b), rear brimlength (c), and front brim length (d) are measured for each vertebralbody as described in (i), and by substituting a, b, c and d in thediscriminant formula determined in (ii), the discriminant values for "nodeformation", wedge-shape vertebrae, fish vertebrae, and flat vertebraeare determined respectively, and the type which has the highestnumerical value is judged to be the vertebral body deformation type. Forexample, when the vertebral body deformation type of the third lumbarvertebrae of the patient is to be judged, the respective measured valuesof a, b, c and d are substituted in the discriminant formula of thethird lumbar vertebrae determined in (ii) as a matter of course. Havingdescribed above the method for judging, the present invention is notlimited to the above classification of the four vertebral deformationtypes of "no deformation", wedge-shaped vertebrae, fish vertebrae andflat vertebrae from the four measured values of central length (a),vertebral body width (b), rear brim length (c), and front brim length(d), but it is also possible to classify the vertebral body deformationtypes by use of the discriminant function as described below.

(A) Method for classifying the three vertebral body deformation typesfrom three or four measured values.

For example, in the first to the eleventh thoracic vertebrae, in whichfish vertebrae do not generally exist, classification is required foronly the three types of "no deformation", wedge-shaped vertebrae, andflat vertebrae. It may also arise that sufficient measured values of a,b, c, and d of fish vertebrae cannot be obtained for determining thediscriminant formula even if a classification of the four typesincluding fish vertebrae is desired.

In such cases, it is possible to determine the discriminant formula forclassifying the three types of "no deformation", wedge-shaped vertebrae,and flat vertebrae from the four measured values of the central length(a), vertebral body width (b), rear brim length (c), and front brimlength (d), or from three of these four measured values, for example,three measured values of a, c, and d.

(B) Method for classifying two vertebral body deformation types from twoto four measured values.

Fish vertebrae and flat vertebrae can be judged relatively easily evenwhen visually observed, and rarely occur, and therefore, in some casesthey are difficult to judge with the use of a discriminant formula.Accordingly, when it is desired to classify only "no deformation" andwedge-shaped vertebrae by use of a discriminant formula, three, forexample, a, c and d, or two, for example, measured values of c and d,can be used to determine the discriminant formula.

Also, in such a case, it is possible to determine the discriminant valuefor classifying "no deformation" and wedge-shaped vertebrae by using asingle variate discriminant function of c/d.

Specifically speaking, the discriminant function is represented by thefollowing formula in which the ratio (c/d) of c and d measured from atleast five profile X-ray images in each of two types of "wedge-shapedvertebrae" and "no deformation" and the ratio (c/d) of less than z₅obtained from the vertebral body to be judged is judged as "nodeformation" and the ratio (c/d) equal to or larger than z₅ is judged as"wedge-shaped vertebrae".

(i) When the standard deviation σhd 1 of c/d of at least five profileX-ray image of "wedge-type vertebrae" is substantially the same as thestandard deviation σ₂ of c/d of at least five profile X-ray images of"no deformation". ##EQU3## wherein μ₁ and μ₂ are averages of c/drelating to the profile X-ray images of "wedge-shaped vertebrae" and "nodeformation", respectively, π₁ and π₂ are numbers of the X-ray images of"wedge-type vertebrae" and "no deformation", respectively, μ is anaverage of μ₁ and μ₂, and μ is an average of σ₁ and σ₂ ; and

(ii) When σ₁ and σ₂ are substantially different, ##EQU4## wherein μ₁ andμ₂ are averages of c/d relating to the profile X-ray images of"wedge-shaped vertebrae" and "no deformation", respectively, π₁ and π₂are numbers of the X-ray images of "wedge-type vertebrae" and "nodeformation", respectively.

The apparatus for judging the deformation of vertebral body according tothe present invention is used for the practice of the above-mentionedmethod of the present invention. This apparatus is basically composed ofan inputting means for at least two indices of a, b, c, and d, anarithmetic means for effecting necessary operations for thediscrimination, a discriminating means by using the calculation results,a means for inputting the discriminant function and/or standardnecessary for the calculation and discrimination, and an output meansfor outputting the judgment result.

As the inputting means, a rule means, a digitizer means, an imageprocessing means in which an image inputting means such as a TV camerais used.

In the preferred embodiment of the present apparatus, c/d, a/c, and a/dare determined by the arithmetic means, and c, d, σ_(c), σ_(d), and β₁-β₆ are inputted as discriminating standards by the discriminatingstandard inputting means, and the discriminating means can discriminatethe results by these standards. Furthermore, the present apparatus canbe further provided with a means for obtaining the discriminatingstandards from a number of the profile X-ray images having nosubstantial deformation. Furthermore, the present apparatus can beoptionally provided with an arithmetic means capable of discriminatingtwo groups with two variants, which are used for determining the indicesβ₁ to β₆, or of discriminating two groups with one variant. In thiscase, the data of at least two types of the four types of the vertebralbody, i.e., "wedge-shaped vertebrae", "fish vertebrae", "flatvertebrae", and "no deformation" should be input.

In another preferred embodiment of the present apparatus, the arithmeticmeans is connected to a discriminating standard input means forinputting the discriminant function, whereby the arithmetic meanscalculates the discriminating values with said discriminant function andthe discriminating means determine the type of the vertebral body basedon the maximum discriminating value. In this case, the present apparatusis provided with a function capable of discriminating the four types ofthe vertebral body, "wedge-shaped vertebrae", "fish vertebrae", "flatvertebrae", and "no deformation" from four one-dimensional formulascontaining a total of four variables a, b, c and d. Furthermore, thereis also the apparatus which is capable of judging the two types of thevertebral body with one variant.

According to the first aspect of the judgment method and the apparatusof the present invention, the type of vertebral body deformation can beobjectively evaluated, and also the change in the said deformation typeand the progress over a period of time of the vertebral body deformationcan be judged.

Also, the present method and apparatus is very useful for determiningthe progress of bone disease such as osteoporosis, etc., and forconfirmation of the effect of therapy.

According to the second aspect of the judgment method and apparatus ofthe present invention, the type of vertebral body deformation can beobjectively evaluated, and further the change in the type of deformationtype and the progress over a period of time of the vertebral bodydeformation can be judged.

Also, the present method and apparatus is very useful for determiningthe progress of bone disease such as osteoporosis, etc., and forconfirmation of the effect of therapy.

EXAMPLES

The present invention will now be further illustrated by, but is by nomeans limited to, the following Examples.

EXAMPLE 1

From the profile X-ray images of thoracic and lumbar vertebrae, with theeighth thoracic vertebrae and the third lumbar vertebrae as the center,of 50 to 75 year old women, the front brim length (d), central length(a), rear brim length (c), and vertebral body width (b) were measuredfor each vertebral body, and for the vertebral bodies classified by aphysician as "no deformation", the average values (x) and standarddeviations (σ) for the respective vertebral bodies of the measuredvalues of a, b, c and d, and the calculated values of c/d, are as shownin Table 1.

                                      TABLE 1                                     __________________________________________________________________________                                  Unit: mm                                                Data a     b     c     d     c/d                                      Site    number                                                                             - x                                                                              σ                                                                          - x                                                                              σ                                                                          - x                                                                              σ                                                                          - x                                                                              σ                                                                          - x                                                                              σ                               __________________________________________________________________________     2nd                                                                             thoracic                                                                            11  18.27                                                                            3.02                                                                             25.40                                                                            4.03                                                                             21.60                                                                            3.80                                                                             18.69                                                                            2.97                                                                             1.15                                                                             0.11                                     vertebrae                                                                   3rd                                                                             thoracic                                                                            56  17.08                                                                            2.20                                                                             25.30                                                                            2.67                                                                             21.03                                                                            2.44                                                                             18.46                                                                            2.10                                                                             1.14                                                                             0.11                                     vertebrae                                                                   4th                                                                             thoracic                                                                           141  17.83                                                                            2.25                                                                             26.65                                                                            2.60                                                                             21.28                                                                            2.17                                                                             18.41                                                                            2.07                                                                             1.16                                                                             0.10                                     vertebrae                                                                   5th                                                                             thoracic                                                                           194  18.20                                                                            2.12                                                                             27.22                                                                            2.52                                                                             21.74                                                                            2.21                                                                             18.62                                                                            2.05                                                                             1.17                                                                             0.09                                     vertebrae                                                                   6th                                                                             thoracic                                                                           210  18.87                                                                            1.90                                                                             28.31                                                                            2.70                                                                             22.02                                                                            1.81                                                                             18.67                                                                            2.02                                                                             1.18                                                                             0.11                                     vertebrae                                                                   7th                                                                             thoracic                                                                           210  19.28                                                                            1.77                                                                             29.57                                                                            2.64                                                                             22.49                                                                            1.95                                                                             18.99                                                                            2.12                                                                             1.19                                                                             0.11                                     vertebrae                                                                   8th                                                                             thoracic                                                                           207  19.78                                                                            1.69                                                                             30.79                                                                            2.75                                                                             22.92                                                                            1.88                                                                             19.74                                                                            2.05                                                                             1.16                                                                             0.13                                     vertebrae                                                                   9th                                                                             thoracic                                                                           220  20.07                                                                            1.99                                                                             31.78                                                                            2.95                                                                             23.30                                                                            1.88                                                                             20.52                                                                            2.19                                                                             1.14                                                                             0.10                                     vertebrae                                                                  10th                                                                             thoracic                                                                           229  21.03                                                                            2.07                                                                             32.89                                                                            3.19                                                                             24.32                                                                            2.21                                                                             21.44                                                                            2.22                                                                             1.14                                                                             0.10                                     vertebrae                                                                  11th                                                                             thoracic                                                                           214  22.04                                                                            2.42                                                                             33.83                                                                            3.06                                                                             26.11                                                                            2.57                                                                             22.25                                                                            2.37                                                                             1.18                                                                             0.11                                     vertebrae                                                                  12th                                                                             thoracic                                                                           194  24.16                                                                            2.22                                                                             34.52                                                                            3.26                                                                             28.20                                                                            3.00                                                                             24.52                                                                            2.45                                                                             1.15                                                                             0.11                                     vertebrae                                                                   1st                                                                             lumbar                                                                             215  26.18                                                                            2.34                                                                             34.98                                                                            2.94                                                                             30.32                                                                            2.68                                                                             26.72                                                                            2.36                                                                             1.14                                                                             0.09                                     vertebrae                                                                   2nd                                                                             lumbar                                                                             233  26.57                                                                            2.76                                                                             36.09                                                                            3.31                                                                             30.88                                                                            2.72                                                                             27.55                                                                            2.83                                                                             1.13                                                                             0.11                                     vertebrae                                                                   3rd                                                                             lumbar                                                                             237  27.10                                                                            2.78                                                                             37.44                                                                            3.21                                                                             30.58                                                                            2.76                                                                             28.62                                                                            3.14                                                                             1.07                                                                             0.11                                     vertebrae                                                                   4th                                                                             lumbar                                                                             251  26.68                                                                            3.11                                                                             37.69                                                                            3.02                                                                             28.07                                                                            2.72                                                                             28.08                                                                            3.27                                                                             1.00                                                                             0.09                                     vertebrae                                                                   5th                                                                             lumbar                                                                             225  25.91                                                                            2.85                                                                             37.72                                                                            3.05                                                                             26.34                                                                            2.54                                                                             27.83                                                                            3.37                                                                             0.95                                                                             0.12                                     vertebrae                                                                  __________________________________________________________________________

EXAMPLE 2

From the profile X-ray image of the thoracic and lumber vertebrae of a70 year old osteoporosis patient (woman), the center length (a),vertebral body width (b), rear brim length (c), and front brim length(d) were measured for each vertebral body, and c/d, a/c and a/d werecalculated. The results of the judgment of the presence of deformationof each vertebral body, and the type of change, are shown in Table 2.The judgment was made according to the judgment standard shown in Table2. The same standards were also used in Examples 3 and 4.

                                      TABLE 2                                     __________________________________________________________________________                                   Presence of                                                                   deformation                                    Measurement                    Type of                                        site:   a  b  c  d   c/d                                                                              a/c a/d                                                                              deformation                                    __________________________________________________________________________    Site:                                                                          5th                                                                             thoracic                                                                           13.5                                                                             28.8                                                                             20.6                                                                             15.9                                                                              1.30                                                                             0.65                                                                              0.85                                                                             Nor deformation                                   vertebrae                                                                   6th                                                                             thoracic                                                                           13.1                                                                             33.3                                                                             22.0                                                                             13.5                                                                              1.63                                                                             0.60                                                                              0.97                                                                             Type I                                            vertebrae                                                                   7th                                                                             thoracic                                                                           13.3                                                                             36.5                                                                             21.3                                                                             17.1                                                                              1.25                                                                             0.63                                                                              0.78                                                                             Type II                                           vertebrae                                                                   8th                                                                             thoracic                                                                           12.9                                                                             38.2                                                                             21.8                                                                             13.2                                                                              1.64                                                                             0.59                                                                              0.97                                                                             Type I                                            vertebrae                                                                   9th                                                                             thoracic                                                                           21.3                                                                             35.9                                                                             23.8                                                                             22.5                                                                              1.05                                                                             0.90                                                                              0.95                                                                             No deformation                                    vertebrae                                                                  10th                                                                             thoracic                                                                           17.8                                                                             38.5                                                                             23.8                                                                             21.8                                                                              1.09                                                                             0.75                                                                              0.82                                                                             "                                                 vertebrae                                                                  11th                                                                             thoracic                                                                           15.2                                                                             38.2                                                                             25.8                                                                             16.8                                                                              1.53                                                                             0.59                                                                              0.91                                                                             Type I                                            vertebrae                                                                  12th                                                                             thoracic                                                                           20.1                                                                             38.7                                                                             29.1                                                                             16.9                                                                              1.73                                                                             0.69                                                                              1.19                                                                             Type I                                            vertebrae                                                                   1st                                                                             lumbar                                                                             12.7                                                                             40.4                                                                             27.3                                                                             17.8                                                                              1.53                                                                             0.46                                                                              0.71                                                                             Type I                                            vertebrae                                                                   2nd                                                                             lumbar                                                                             18.7                                                                             40.8                                                                             27.9                                                                             22.0                                                                              1.27                                                                             0.67                                                                              0.85                                                                             No deformation                                    vertebrae                                                                   3rd                                                                             lumbar                                                                             13.7                                                                             45.4                                                                             28.1                                                                             25.2                                                                              1.11                                                                             0.49                                                                              0.54                                                                             Type II                                           vertebrae                                                                   4th                                                                             lumbar                                                                             17.2                                                                             42.4                                                                             26.5                                                                             31.2                                                                              0.85                                                                             0.65                                                                              0.55                                                                             Type II                                           vertebrae                                                                   5th                                                                             lumbar                                                                             21.6                                                                             42.5                                                                             23.7                                                                             23.8                                                                              1.00                                                                             0.91                                                                              0.91                                                                             No deformation                                    vertebrae                                                                  __________________________________________________________________________

EXAMPLE 3

From the profile X-ray image, with the third lumbar vertebrae as thecenter, of ten osteoporosis patients (women) 59 to 76 year old, thecentral length (a), vertebral body width (b), rear brim length (c), andfront brim length (d) of the third lumber vertebrae were measured andc/d, a/c, and a/d were calculated. The results of the judgment of thepresence of deformation, and the type of deformation, are shown in Table3.

                                      TABLE 3                                     __________________________________________________________________________                                   Presence of                                                                   deformation                                    Measurement                    Type of                                        site:  a  b   c  d   c/d                                                                              a/c a/d                                                                              deformation                                    __________________________________________________________________________    Case (age):                                                                    1 (59)                                                                              31.4                                                                             38.6                                                                              38.0                                                                             34.2                                                                              1.11                                                                             0.83                                                                              0.92                                                                             No deformation                                  2 (63)                                                                              28.0                                                                             40.2                                                                              33.3                                                                             32.4                                                                              1.03                                                                             0.84                                                                              0.86                                                                             "                                               3 (64)                                                                              26.9                                                                             41.1                                                                              30.1                                                                             28.4                                                                              1.06                                                                             0.90                                                                              0.95                                                                             "                                               4 (66)                                                                              18.3                                                                             41.0                                                                              31.6                                                                             21.4                                                                              1.47                                                                             0.58                                                                              0.85                                                                             Type I                                          5 (76)                                                                              20.8                                                                             34.7                                                                              26.3                                                                             16.6                                                                              1.59                                                                             0.79                                                                              1.25                                                                             "                                               6 (65)                                                                              21.2                                                                             37.6                                                                              32.7                                                                             17.4                                                                              1.88                                                                             0.65                                                                              1.22                                                                             "                                               7 (68)                                                                              16.6                                                                             40.7                                                                              25.6                                                                             24.8                                                                              1.03                                                                             0.65                                                                              0.67                                                                             Type II                                         8 (66)                                                                              20.4                                                                             41.4                                                                              29.6                                                                             30.9                                                                              0.96                                                                             0.69                                                                              0.66                                                                             "                                               9 (72)                                                                              14.2                                                                             33.8                                                                              22.4                                                                             16.7                                                                              1.34                                                                             0.63                                                                              0.85                                                                             Type III                                       10 (62)                                                                              21.2                                                                             31.9                                                                              23.8                                                                             21.7                                                                              1.09                                                                             0.89                                                                              0.97                                                                             "                                              __________________________________________________________________________

EXAMPLE 4

From the profile X-ray image, with the eighth thoracic vertebrae and thethird lumbar vertebrae as the center, of a 67 year old osteoporosispatient (woman), the center length (a), vertebral body width (b), rearbrim length (c), and front brim length (d) from the sixth thoracicvertebrae to the fifth lumbar vertebrae were measured, and c/d, a/c, anda/d were calculated to judge the presence of deformation and the type ofdeformation. Six months later, the profile X-ray image of the same sitewas photographed again to judge the presence of deformation and the typeof deformation according to the same method, and at the same time, thechange in the ratios of a, b, c and d were calculated. The results areshown in Table 4.

                                      TABLE 4                                     __________________________________________________________________________            At initiation of experiment                                                                        Type of                                                                             After 6                                                                 deforma-                                                                            months                                             a  b  c  d  c/d                                                                              a/c                                                                              a/d                                                                              tion  a  b                                       __________________________________________________________________________     6th                                                                             thoracic                                                                           15.8                                                                             30.8                                                                             23.2                                                                             15.9                                                                             1.46                                                                             0.68                                                                             0.99                                                                             Type I                                                                              16.7                                                                             29.0                                       vertebrae                                                                   7th                                                                             thoracic                                                                           19.6                                                                             32.1                                                                             26.0                                                                             19.5                                                                             1.33                                                                             0.75                                                                             1.01                                                                             No defor-                                                                           19.6                                                                             33.8                                       vertebrae                 mation                                            8th                                                                             thoracic                                                                           16.1                                                                             31.7                                                                             22.1                                                                             16.5                                                                             1.37                                                                             0.73                                                                             0.98                                                                             No defor-                                                                           14.7                                                                             32.7                                       vertebrae                 mation                                            9th                                                                             thoracic                                                                           21.6                                                                             35.2                                                                             26.5                                                                             23.6                                                                             1.12                                                                             0.82                                                                             0.92                                                                             No defor-                                                                           19.9                                                                             36.0                                       vertebrae                 mation                                           10th                                                                             thoracic                                                                           16.6                                                                             38.1                                                                             23.6                                                                             14.4                                                                             1.63                                                                             0.70                                                                             1.15                                                                             Type I                                                                              14.0                                                                             35.2                                       vertebrae                                                                  11th                                                                             thoracic                                                                           24.2                                                                             37.8                                                                             29.1                                                                             25.4                                                                             1.15                                                                             0.83                                                                             0.95                                                                             No defor-                                                                           24.1                                                                             36.0                                       vertebrae                 mation                                           12th                                                                             thoracic                                                                           26.3                                                                             37.8                                                                             31.3                                                                             27.5                                                                             1.14                                                                             0.84                                                                             0.96                                                                             No defor-                                                                           25.9                                                                             39.3                                       vertebrae                 mation                                            1st                                                                             lumbar                                                                             27.5                                                                             35.1                                                                             33.3                                                                             28.1                                                                             1.19                                                                             0.82                                                                             0.98                                                                             No defor-                                                                           22.9                                                                             34.6                                       vertebrae                 mation                                            2nd                                                                             lumbar                                                                             24.0                                                                             38.7                                                                             30.4                                                                             26.8                                                                             1.14                                                                             0.79                                                                             0.89                                                                             No defor-                                                                           20.0                                                                             35.6                                       vertebrae                 mation                                            3rd                                                                             lumbar                                                                             14.3                                                                             41.6                                                                             21.4                                                                             20.7                                                                             1.03                                                                             0.67                                                                             0.69                                                                             Type III                                                                             9.1                                                                             39.8                                       vertebrae                                                                   4th                                                                             lumbar                                                                             19.0                                                                             40.0                                                                             29.1                                                                             22.1                                                                             1.32                                                                             0.65                                                                             0.86                                                                             No defor-                                                                           19.2                                                                             36.4                                       vertebrae                 mation                                            5th                                                                             lumbar                                                                             19.3                                                                             38.4                                                                             26.4                                                                             26.3                                                                             1.00                                                                             0.73                                                                             0.73                                                                             Type II                                                                             18.6                                                                             38.4                                       vertebrae                                                                  __________________________________________________________________________            After 6                                                                       months                                                                                       Type of                                                                             Change in ratio                                                         deforma-                                                                            (%)                                                      c  d  c/d                                                                              a/c                                                                              a/d                                                                              tion  a  b  c  d                                       __________________________________________________________________________     6th                                                                             thoracic                                                                           22.4                                                                             15.0                                                                             1.49                                                                             0.74                                                                             1.11                                                                             Type I                                                                              105                                                                              94 96 94                                         vertebrae                                                                   7th                                                                             thoracic                                                                           22.3                                                                             17.3                                                                             1.29                                                                             0.88                                                                             1.14                                                                             No defor-                                                                           100                                                                              105                                                                              85 88                                         vertebrae           mation                                                  8th                                                                             thoracic                                                                           21.9                                                                             16.3                                                                             1.34                                                                             0.67                                                                             0.90                                                                             No defor-                                                                           91 103                                                                              99 98                                         vertebrae           mation                                                  9th                                                                             thoracic                                                                           24.9                                                                             22.2                                                                             1.12                                                                             0.80                                                                             0.89                                                                             No defor-                                                                           91 102                                                                              94 94                                         vertebrae           mation                                                 10th                                                                             thoracic                                                                           22.9                                                                             14.5                                                                             1.58                                                                             0.61                                                                             0.97                                                                             Type I                                                                              84 92 97 100                                        vertebrae                                                                  11th                                                                             thoracic                                                                           28.6                                                                             25.0                                                                             1.14                                                                             0.84                                                                             0.96                                                                             No defor-                                                                           99 95 98 98                                         vertebrae           mation                                                 12th                                                                             thoracic                                                                           30.8                                                                             26.9                                                                             1.15                                                                             0.84                                                                             0.96                                                                             No defor-                                                                           98 103                                                                              98 97                                         vertebrae           mation                                                  1st                                                                             lumbar                                                                             31.8                                                                             26.4                                                                             1.21                                                                             0.72                                                                             0.87                                                                             No defor-                                                                           83 98 95 94                                         vertebrae           mation                                                  2nd                                                                             lumbar                                                                             23.6                                                                             20.8                                                                             1.13                                                                             0.85                                                                             0.96                                                                             Type III                                                                            83 92 77 77                                         vertebrae                                                                   3rd                                                                             lumbar                                                                             21.1                                                                             20.3                                                                             0.87                                                                             0.43                                                                             0.44                                                                             "     63 95 98 98                                         vertebrae                                                                   4th                                                                             lumbar                                                                             27.2                                                                             22.6                                                                             1.20                                                                             0.71                                                                             0.85                                                                             No defor-                                                                           101                                                                              91 93 102                                        vertebrae           mation                                                  5th                                                                             lumbar                                                                             26.4                                                                             25.4                                                                             1.04                                                                             0.70                                                                             0.73                                                                             Type II                                                                             96 99 100                                                                              96                                         vertebrae                                                                  __________________________________________________________________________

The second lumbar vertebrae changed from a "no deformation"classification to a type III (flat vertebrae) within six months.

Although not showing a clear deformation, the conditions of the frontbrim and rear brim of the seventh thoracic vertebrae, and the center ofthe tenth thoracic vertebrae, tend to have worsened. Also, theconditions of the centers of the tenth thoracic vertebrae and the thirdlumbar vertebrae had further worsened.

On the other hand, substantially no change has occurred in the sixth,eighth, ninth, eleventh, and twelfth thoracic vertebrae, or in thefourth and fifth lumbar vertebrae.

EXAMPLE 5

For 186 vertebral bodies, including 6 vertebral bodies judged aswedge-shaped vertebrae, 25 vertebral bodies judged as fish vertebrae,eight vertebral bodies judged as flat vertebrae and 147 vertebral bodiesjudged as "no deformation" according to visual observation by aphysician of a profile X-ray image, with the third lumbar vertebrae asthe center, of osteoporosis patients (women), eight points of 1 to 8shown in FIG. 4 were input through a digitizer into a computer tomeasure the central length (a), vertebral body width (b), rear brimlength (c), and front brim length (d), and calculation was performed bya computer by inputting the above a, b, c, and d into a multivariatediscriminant analytical program in the BMD multivariate analyticalprogram of IBM Co. to obtain the coefficients and constants of thediscriminant formula as shown in Table 5.

                                      TABLE 5                                     __________________________________________________________________________              1        2      3      4                                                      (wedge-shaped                                                                          (fish  (flat  (no defor-                                   FUNCTION  vertebrae)                                                                             vertebrae)                                                                           vertebrae)                                                                           mation)                                      __________________________________________________________________________    COEFFICIENT                                                                   1 (a)     1.41660  0.14656                                                                              -0.19733                                                                             1.94241                                      2 (b)     3.31142  3.63664                                                                              3.37930                                                                              3.51934                                      3 (c)     2.39311  1.77030                                                                              1.42894                                                                              1.43377                                      4 (d)     -0.73812 1.23660                                                                              1.18794                                                                              0.60223                                      CONSTANT  -100.52945                                                                             -114.00328                                                                           -89.05205                                                                            -123.11888                                   __________________________________________________________________________

The discriminant value for each vertebral body was calculated bysubstituting the measured values of a, b, c, and d, into the above fourdiscriminant formulae, and the type having the maximum numerical valuewas judged to be the vertebral body deformation type.

The coincidence of the vertebral body deformation type thus judgedaccording to the discriminant formula with the vertebral bodydeformation type according to the physician's judgment is shown in Table6, indicating a good coincidence between both judgments. The coincidenceratio of the respective types is 94.6%.

                                      TABLE 6                                     __________________________________________________________________________    Discriminant                                                                             Wedge-shaped                                                                          Fish Flat No defor- Coincidence                            analysis:  vertebrae                                                                             vertebrae                                                                          vertebrae                                                                          mation                                                                              Total                                                                             ratio (%)                              __________________________________________________________________________    Physician's judgments:                                                        Wedge-shaped                                                                             6       0    0    0      6  100.0                                  vertebrae                                                                     Fish vertebrae                                                                           0        ○23                                                                        2    0     25  92.0                                   Flat vertebrae                                                                           0       1    7    0      8  87.2                                   No deformation                                                                           2       1    0      ○140                                                                       147 95.2                                   __________________________________________________________________________     The mark ◯ shows the number of vertebral bodies for which bot     judgments coincide.                                                      

EXAMPLE 6

From a profile X-ray image, with the third lumbar vertebrae as thecenter, of 10 osteoporosis patients (women), the central length (a),vertebral body width (b), rear brim length (c), and front brim length(d) of the third lumbar vertebrae were measured and substituted in thediscriminant formula determined in Example 5 (coefficients and constantsare shown in Table 5) to calculate the respective discriminant values,and the type having the maximum numerical value was judged to be thevertebral body deformation type. The results are shown in Table 7.

                                      TABLE 7                                     __________________________________________________________________________    Vertebral body mea-                                                                          Discriminant values                                            sured values (mm)                                                                            Wedge-shaped                                                                          Fish Flat No defor-                                                                           Deformation                            No.                                                                              a  b  c  d  vertebrae                                                                             vertebrae                                                                          vertebrae                                                                          mation                                                                              type                                   __________________________________________________________________________    1  27.0                                                                             37.8                                                                             31.6                                                                             27.3                                                                             118.36  117.12                                                                             110.94                                                                             124.11                                                                              No deformation                         2  27.5                                                                             33.4                                                                             32.6                                                                             28.1                                                                             106.30  103.95                                                                             98.35                                                                              115.51                                                                              No deformation                         3  15.9                                                                             40.2                                                                             26.0                                                                             17.0                                                                             104.79  101.57                                                                             101.01                                                                             96.76 Wedge-shaped                                                                  vertebrae                              4  16.9                                                                             35.2                                                                             28.2                                                                             15.6                                                                             95.94   85.70                                                                              85.39                                                                              83.42 Wedge-shaped                                                                  vertebrae                              5  20.5                                                                             40.3                                                                             30.5                                                                             20.0                                                                             120.19  114.28                                                                             110.43                                                                             114.30                                                                              Wedge-shaped                                                                  vertebrae                              6  19.6                                                                             38.6                                                                             28.1                                                                             26.9                                                                             102.45  112.25                                                                             109.63                                                                             107.29                                                                              Fish vertebrae                         7  20.8                                                                             36.9                                                                             28.7                                                                             30.0                                                                             97.67   111.14                                                                             108.19                                                                             106.36                                                                              Fish vertebrae                         8  21.6                                                                             32.6                                                                             30.8                                                                             30.8                                                                             89.00   100.33                                                                             97.45                                                                              96.28 Fish vertebrae                         9  13.2                                                                             34.0                                                                             21.3                                                                             17.3                                                                             68.96   70.68                                                                              74.23                                                                              63.14 Flat vertebrae                         10 18.8                                                                             31.0                                                                             21.8                                                                             21.5                                                                             65.05   66.67                                                                              68.69                                                                              66.70 Flat vertebrae                         __________________________________________________________________________

EXAMPLE 7

From vertebral body profile X-ray images with the eighth thoracicvertebrae and the third thoracic vertebrae as the centers thereof,respectively, according to a physician's judgment, as shown in Table 8,from the sixth thoracic vertebrae to the third thoracic vertebrae, 257vertebral bodies of wedge-shaped vertebrae and 2,157 vertebral bodies of"no deformation" were selected, and the central length (a), vertebralwidth (b), rear brim length (c), and front brim length (d) of eachvertebral body were measured as in Example 5, and in addition, the c/dwas calculated.

For discriminating wedge-shaped vertebrae from "no deformation" with onevariate of c/d, the value of c/d for each vertebral body was input tothe one variate discriminant analytical program in the BMD multivariateanalytical program of IBM Co. to obtain the discriminant values shown inTable 8. The coincidence with the physicians judgment whendiscrimination was made between wedge-shaped vertebrae and "nodeformation" by use of these discriminant values is shown in Table 8.For all vertebral bodies, the coincidence ratio of "no deformation" was98.15%, and the coincidence ratio of wedge-shaped vertebrae 87.16%, thusgiving good results.

                                      TABLE 8                                     __________________________________________________________________________                           Coincidence with                                                              physician's judgment                                   Number of vertebral    Wedge-shaped                                           bodies used for Discriminant                                                                         vertebrae                                                                              No deformation                                discrimination  c/d value   Coinci-  Coinci-                                       Wedge-     according to                                                                         Coinci-                                                                            dence                                                                             Coinci-                                                                            dence                                         shaped                                                                             No defor-                                                                           discriminant                                                                         dence                                                                              ratio                                                                             dence                                                                              ratio                                    Site vertebrae                                                                          mation                                                                              function                                                                             number                                                                             (%) number                                                                             (%)                                      __________________________________________________________________________    Th 6 14   209   1.456  11   78.57                                                                             208  99.52                                    Th 7 22   205   1.422  18   81.82                                                                             204  99.51                                    Th 8 25   206   1.399  21   84.00                                                                             204  99.03                                    Th 9 19   217   1.388  18   94.74                                                                             212  97.70                                    Th 10                                                                               9   228   1.420   6   66.67                                                                             226  99.12                                    Th 11                                                                              30   214   1.422  22   73.33                                                                             207  96.73                                    Th 12                                                                              55   193   1.363  51   92.73                                                                             186  96.37                                    L 1  52   214   1.341  49   94.23                                                                             212  99.07                                    L 2  25   238   1.406  23   92.00                                                                             229  96.22                                    L 3   6   233   1.407   5   83.33                                                                             229  98.38                                    Total/                                                                             257  2,157 1.402  224  87.16                                                                             2,117                                                                              98.15                                    average                                                                       __________________________________________________________________________     Th: thoracic vertebrae                                                        L: lumbar vertebrae                                                      

EXAMPLE 8

From the profile X-ray images, with the eighth thoracic vertebrae as thecenter, of 10 osteoporosis patients (women), as described in Example 5,the center length (a), vertebral body width (b), rear brim length (c),and front brim length (d) of the eighth thoracic vertebrae weremeasured, and in addition, the c/d was calculated. The results are shownin Table 9. Since these vertebral bodies were neither clearly fishvertebrae nor flat vertebrae, a discrimination between wedge-shapedvertebrae and "no deformation" by the c/d determined in Example 7 wasconducted. The results are shown in the right hand column in Table 9.

                  TABLE 9                                                         ______________________________________                                        Vertebrae body measured                                                       values (mm)              Deformation                                          No.  a       b       c     d     c/d   type                                   ______________________________________                                        1    20.0    22.5    24.7  16.5  1.50  Wedge-shaped                                                                  vertebrae                              2    21.6    30.2    24.4  21.3  1.14  No deformation                         3    17.5    32.9    21.7  13.6  1.60  Wedge-shaped                                                                  vertebrae                              4    17.7    38.3    29.6  15.6  1.90  Wedge-shaped                                                                  vertebrae                              5    22.0    28.8    23.8  19.2  1.24  No deformation                         6    12.9    38.2    21.8  13.2  1.64  Wedge-shaped                                                                  vertebrae                              7    21.0    28.3    24.5  21.2  1.15  No deformation                         8    18.9    32.0    22.4  18.5  1.21  "                                      9    19.8    30.8    24.3  18.7  1.30  "                                      10   19.3    31.3    22.2  15.6  1.43  Wedge-shaped                                                                  vertebrae                              ______________________________________                                    

We claim:
 1. A method for judging deformation of a vertebral body in asubject comprising the steps of:(i) measuring a central length (a), arear brim length (c) and a front brim length (d) from a plurality ofprofile X-ray images obtained from vertebral bodies having substantiallyno deformation at a portion corresponding to a portion of said vertebralbody to be judged, storing the measurements in a memory, and determiningvalues of c/d, a/c and a/d, the average values c and d of the rear brimlengths (c) and front brim lengths (d), respectively, and the standarddeviations σ_(c) and σ_(d) of the values c and d, respectively; (ii)measuring a, c, and d from a plurality of the profile X-ray imagesobtained from vertebral bodies having at least one deformation of a"wedge-shaped" vertebrae, and "inverse wedge-shaped" vertebrae, a "fish"vertebrae, and a "flat" vertebrae, storing the measurements in saidmemory, and determining values of c/d, a/c, a/d, and c, d, σ_(c), andσ_(d) ; (iii) preparing a judgment standard from the data obtained insteps (i) and (ii) for determining the "no deformation" vertebrae,"wedge-shaped" vertebrae. "inverse wedge-shaped" vertebrae, "fish"vertebrae, and "flat" vertebrae; (iv) measuring a, c, and d from aprofile X-ray image of said vertebral body to be judged, storing themeasurements in said memory, and determining c/d, a/c, and a/d; and (v)classifying deformation of said vertebral body to be judged from c/d inthe case of "wedge-shaped", and "inverse wedge-shaped" vertebrae, fromc, d, σ_(c), σ_(d), and c/d in the case of "flat" vertebrae, and from c,d, σ_(c), σ_(d), a/c, a/d, and c/d in the case of the "no deformation"and "fish" vertebrae, in order to diagnose deformation and to monitorthe effect of therapy on said vertebral body to be judged; wherein saidstep (v) is carried out according to the following sub-steps: (i) c/d≧β₁. . . wedge-shaped vertebrae (or anterior wedge fracture) (ii) c/d≦β₂ .. . inverse wedge-shaped vertebrae (or inverse anterior wedge fracture)(iii) c<c-β₃ σ_(c), d<d-β₄ σ_(d), and β₂ <c/d<β₁ . . . flat vertebrae(or compression fracture) (iv) β₂ <c/d<β₁, a/c≦β₅, a/d≦β₆ and, c≧c-β₃σ_(c) and/or d≧d-β₄ σ_(d) . . . fish vertebrae (or central biconcavefracture) (v) β₂ <c/d<β₁, c≧c-β₃ σ_(c) and/or d≧d-β₄ σ_(d), and a/c>β₅and/or a/d>β₆ . . . No deformation (or no fracture), wherein β₁ to β₆are selected as follows: 1.25≦β₁ ≦1.55, 0.6≦β₂ ≦0.8, 1≦β₃ ≦2.5, 1≦β₄≦2.5, 0.65≦β₅ ≦0.9, and 0.65≦β₆ ≦0.9; and wherein β₁ to β₆ are 1.33≦β₁≦1.5, 0.65≦β₂ ≦0.75, 1.25≦β₃ ≦2.25, 1.25≦β₄ ≦2.25, 0.7≦β₅ ≦0.85, and0.7≦β₆ ≦0.85.
 2. A method as claimed in claim 1, wherein the measuringstep is carried out by a rule means, a digitizer means, or a means forautomatically measuring the lengths from image treatment by memorizingthe X-ray image with an X-ray image automatic input means.
 3. A methodas claimed in claim 1 wherein classifying deformation of the vertebralbody is carried out as follows:(i) c/d≧β₁ . . . wedge-shaped vertebrae(or anterior wedge fracture) (ii) c/d≦β₂ . . . inverse wedge-shapedvertebrae (or inverse anterior wedge fracture) (iii) c<c-β₃ σ_(c),d<d-β₄ σ_(d), and β₂ <c/d<β₁ . . . flat vertebrae (or compressionfracture) (iv) β₂ <c/d<β₁, a/c≦β₅, a/d≦β₆ and, c≧c-β₃ σ_(c) and/ord≧d-β₄ σ_(d) . . . fish vertebrae (or central biconcave fracture) (v) β₂<c/d<β₁, c≧c-β₃ σ_(c) and/or d≧d-β₄ π_(d), and a/c>β₅ and/or a/d>β₆ . .. No deformation (or no fracture), wherein β₁ to β₆ are selected asfollows: 1.25≦β₁ ≦1.55, 0.6≦β₂ ≦0.8, 1≦β₃ ≦2.5, 1≦β₄ ≦2.5, 0.65≦β₅ ≦0.9,and 0.65≦β₆ ≦0.9.
 4. A method as claimed in claim 3, wherein β₁ is 1.4,β₂ is 0.7, β₃ is 2, β₄ is 1.5, β₅ is 0.8, and β₆ is 0.8.
 5. A method asclaimed in claim 3, wherein at least one of β₁ to β₆ are determined by adiscriminant function capable of discriminating two groups with one ortwo variables by using two of a, b, c, and d or a ratio of at least twovariables thereof, which are obtained by measuring at least five profileX-ray images in each of two types selected from four types,"wedge-shaped vertebrae", "fish vertebrae", "flat vertebrae", and "nodeformation".
 6. A method as claimed in claim 5, wherein β₁ is z₅obtained by the following discriminant function using the ratio c/dderived from c and d, which are obtained by measuring at least fiveprofile X-ray images in each of two types selected from "wedge-shaped"vertebrae" and "no deformation":(i) When the standard deviation σ₁ ofc/d at least five profile X-ray images of "wedge-type vertebrae" issubstantially the same as the standard deviation σ₂ of c/d of at leastfive profile X-ray images of "no deformation", ##EQU5## wherein μ₁ andμ₂ are averages of c/d relating to the profile X-ray images of"wedge-shaped vertebrae" and "no deformation", respectively, π₁ and π₂are numbers of the X-ray images of "wedge-type vertebrae" and "nodeformation", respectively, μ is an average of μ₁ and μ₂, and σ is anaverage of σ₁ and σ₂ ; and (ii) When σ₁ and σ₂ are substantiallydifferent, ##EQU6## wherein A, B and C are determined from the followingequations: ##EQU7## wherein μ₁ and μ₂ are averages of c/d relating tothe profile X-ray images of "wedge-shaped vertebrae" and "nodeformation", respectively, π₁ and π₂ are numbers of the X-ray images of"wedge-type vertebrae" and "no deformation", respectively.
 7. Anapparatus for judging deformation of a vertebral body of a subjectcomprising:(i) input means for inputting at least two lengths of acentral length (a), vertebral body width (b), rear brim length (c), andfront brim length (d) from a profile X-ray image of a particularvertebral body to be judged; (ii) arithmetic means for performingcalculations to discriminate between at least two of the followingtypes: "wedge-shaped" vertebrae, "inverse wedge-shaped" vertebrae,"fish" vertebrae, "flat" vertebrae, and "no deformation" vertebrae byusing the above-mentioned input values; (iii) means for discriminatingthe at least two types by using the calculation results; (iv) means forinputting a discriminant standard derived from profile X-ray imageshaving substantially no deformation and necessary for the calculationand discrimination; and (v) output means for outputting the judgmentresult in order to diagnose deformation and to monitor the effect oftherapy on said vertebral body to be judged, wherein said arithmeticmeans performs said calculations based on a central length, vertebralbody width, rear brim length, and front brim length measured fromprofile X-ray images of respective vertebral bodies, corresponding tosaid particular vertebral body of said subject, from a plurality ofother subjects, said vertebral bodies in said other subjects havingsubstantially no deformation, wherein said arithmetic means determinesc/d, a/c, and a/d, said means for inputting a discriminant standardinputs a discriminating standard for c, d, σ_(c), σ_(d), and β₁ to β₆,(where c, d, are average values of c and d, respectively, σ_(c), σ_(d),are standard deviations of c and d, respectively, and β₁ to β₆ areindices) and said discriminating means is based on the followingstandards: (i) c/d≧β₁ . . . "wedge-shaped vertebrae" (ii) c/d≦β₂ . . ."inverse wedge-shaped vertebrae" (iii) c<c-β₃ σ_(c), d<-β₄ σ_(d), and β₂<c/d β₁ . . . "flat vertebrae" (iv) β₂ <c/d<β₁, a/c≦β₅, a/d≦β₆ and,c≧c-β₃ σ_(c) and/or d≧d-β₄ σ_(d) . . . "fish vertebrae" (v) β₂ <c/d<β₁,c≧c-β₃ σ_(c) and/or d≧d-β₄ σ_(d), and a/c>β₅ and/or a/d>β₆ . . . "nodeformation" wherein β₁ to β₆ are 1.25≦β₁ ≦1.55, 0.6≦β₂ ≦0.8, 1≦β₃ ≦2.5,1≦β₄ ≦2.5, 0.65≦β₅ ≦0.9, and 0.65≦β₆ ≦0.9.
 8. An apparatus for judgingdeformation of a vertebral body as claimed in claim 7, wherein a tableis prepared based on said at least two values, the discriminantstandard, said judgment result.
 9. An apparatus for judging deformationof a vertebral body of a subject comprising:(i) input means forinputting at least two of the following values: central length (a),vertebral body width (b), rear rim length (c), and front brim length (d)from a profile X-ray image of a particular vertebral body to be judged;(ii) arithmetic means for performing calculations to discriminatebetween at least two of the following types: "wedge-shaped" vertebrae,"inverse wedge-shaped" vertebrae, "fish" vertebrae, "flat" vertebrae,and "no deformation" vertebrae by using the above-mentioned inputvalues; (iii) means for discriminating the at least two types by usingthe calculations results; (iv) means for inputting a discriminantmathematical function based on measured values from profile X-ray imagesof deformed vertebral bodies and on measured values from profile X-rayimages having substantially no deformation and necessary for thecalculation and discrimination; and (v) output means for outputting thejudgment result in order to diagnose deformation and to monitor theeffect of therapy on said vertebral body to be judged, wherein saidarithmetic means performs said calculations based on a central length,vertebral body width, rear brim length, and front brim length measuredfrom profile X-ray images of vertebral bodies, corresponding to saidparticular vertebral body of said subject, from a plurality of othersubjects, respectively, said vertebral bodies in said other subjectshaving at least two of the following respective deformation types:"wedge-shaped" vertebrae, "flat" vertebrae, "fish" vertebrae, and "nodeformation" vertebrae, wherein said arithmetic means is connected withmeans for inputting a discriminant mathematical function for inputtingthe discriminant function and calculates discriminating valuesrepresenting deformation by using the discriminant mathematicalfunction, whereby the type of the vertebral body to be judged isdetermined according to the type corresponding to a maximumdiscriminating value, and wherein said discriminant mathematicalfunction judges whether the vertebral body to be judged is a"wedge-shaped" vertebrae, "fish" vertebrae, "flat vertebrae" and "nodeformation" from four one-dimensional formulas containing four unknownsa, b, c and d.
 10. An apparatus for judging deformation of a vertebralbody as claimed in claim 9, wherein a table is prepared based on the atleast two values, the discriminant mathematical function, and thejudgment result.
 11. A method for judging deformation of a vertebralbody in a subject comprising the steps of:(i) obtaining at least twoindices by measuring a central length (a), vertebral body width (b),rear brim length (c), and front brim length (d) from a profile X-rayimage of a vertebral body to be judged, and storing said at least twoindices in a memory; (ii) analysing said indices by a discriminantfunction obtained by using at least two indices measured from profileX-ray images of at least one other subject having at least two of thefollowing deformation types: "wedge-shaped" vertebrae, "flat" vertebrae,"fish" vertebrae, and "no deformation"; (iii) classifying a deformationof said vertebral body to be judged from the results of said analysingstep, in order to diagnose the condition of and to monitor the effect oftherapy on said vertebral body to be judged; wherein said discriminantfunction is obtained by using indices a, b, c and d measured from atleast five profile X-ray images of other subjects in each of said fourtypes of vertebrae, and is capable of discriminating said four types ofthe vertebral body using indices a, b, c and d, said discriminantfunction being represented by the following formulae, where thevertebral body is judged from the maximum value of z₁ to z₄ :

    z.sub.1 =a.sub.10 +a.sub.11 x.sub.1 +a.sub.12 x.sub.2 +a.sub.13 x.sub.3 +a.sub.14 x.sub.4

    z.sub.2 =a.sub.20 +a.sub.21 x.sub.1 +a.sub.22 x.sub.2 +a.sub.23 x.sub.3 +a.sub.24 x.sub.4

    z.sub.3 =a.sub.30 +a.sub.31 x.sub.1 +a.sub.32 x.sub.2 +a.sub.33 x.sub.3 +a.sub.34 x.sub.4

    z.sub.4 =a.sub.40 +a.sub.41 x.sub.1 +a.sub.42 x.sub.2 +a.sub.43 x.sub.3 +a.sub.44 x.sub.4

wherein z₁, z₂, z₃, and z₄ are discriminant values of "wedge-shapedvertebrae", "fish vertebrae", "flat vertebrae", and "no deformation",respectively, x₁, x₂, x₃, and x₄ are variables corresponding to acentral length, vertebral body width, rear brim length, and front brimlength, respectively, of the vertebrae to be judged, a₁₀, a₂₀, a₃₀, anda₄₀ are constants, and a₁₁ to a₄₄ are coefficients.
 12. A method asclaimed in claim 11, wherein the measurement is carried out by a rulemeans, a digitizer means, or a means for automatically measuring thelengths from image treatment by memorizing the X-ray image with an X-rayimage automatic input means.
 13. A method for judging deformation of avertebral body in a subject as claimed in claim 11, wherein a table isprepared based on the measurements, the analysis, and the discriminantfunction.
 14. A method for judging deformation of a vertebral body in asubject comprising the steps of:(i) obtaining at least two indices bymeasuring a central length (a), vertebral body width (b), rear brimlength (c), and front brim length (d) from a profile X-ray image on avertebral body to be judged, and storing said at least two indices in amemory; (ii) analysing said indices by a discriminant function obtainedby using at least two indices measured from profile X-ray images of atleast one other subject having at least two of the following deformationtypes: "wedge-shaped" vertebrae, "flat" vertebrae, "fish" vertebrae, and"no deformation"; (iii) classifying a deformation of said vertebral bodyto be judged from the results of said analysing step, in order todiagnose the condition of and to monitor the effect of therapy on saidvertebral body to be judged; wherein said discriminant function isderived from at least two indices obtained by measuring a, b, c, and dfrom at least five profile X-ray images in each of two of said fourtypes, and wherein said four types of vertebral body are capable ofbeing identified and distinguished using as variables said at least twomeasured values or ratios of said at least two measured values; saiddiscriminant function being represented by the following formula inwhich the ratio (c/d) of c and d is measured from at least five profileX-ray images in each of said two of said four types, a ratio value (c/d)of less than z₅ obtained from the vertebral body to be judged beingjudged as "no deformation", and a ratio value (c/d) equal to or largerthan z₅ being judged as "wedge-shaped vertebrae": (i) when the standarddeviation σ₁ of c/d of at least five profile X-ray images of"wedge-shaped vertebrae" is substantially the same as the standarddeviation σ₂ of c/d of at least five profile X-ray images of "nodeformation", ##EQU8## wherein μ₁ and μ₂ are averages of c/d relating tothe profile X-ray images of "wedge-shaped vertebrae" and "nodeformation", representatively, μ is an average of μ₁ and μ₂, and σ isan average of σ₁ and σ₂ ; and (ii) when σ₁ and σ₂ are substantiallydifferent, ##EQU9## wherein A, B and C are determined from the followingequations: ##EQU10## wherein π₁ and π₂ are the numbers of the X-rayimages of "wedge-type vertebrae" and "no deformation", respectively. 15.A method as claimed in claim 14, wherein the measurement is carried outby a rule means, a digitizer means, or a means for automaticallymeasuring the lengths from image treatment by memorizing the X-ray imagewith an X-ray image automatic input means.
 16. A method for judginginformation of a vertebral body in a subject as claimed in claim 14,wherein a table is prepared based on the measurements, the analysis, andthe discriminant function.
 17. A method for judging deformation of avertebral body in a subject comprising the steps of:(i) measuring acentral length (a), a rear brim length (c) and a front brim length (d)from a plurality of profile X-ray images obtained from vertebral bodieshaving substantially no deformation at a portion corresponding to aportion of said vertebral body to be judged, storing the measurements ina memory, and determining values of c/d, a/c and a/d, the average valuesc and d of the rear brim lengths (c) and front brim lengths (d),respectively, and the standard deviations σ_(c) and σ_(d) of the valuesc and d, respectively; (ii) measuring a, c and d from a plurality of theprofile X-ray images obtained from vertebral bodies having at least onedeformation of a "wedge-shaped" vertebrae, and "inverse wedge-shaped"vertebrae, a "fish" vertebrae, and a "flat" vertebrae, storing themeasurements in said memory, and determining values of c/d, a/c, a/d,and c, d, σ_(c), and σ_(d) ; (iii) preparing a judgment standard fromthe data obtained in steps (i) and (ii) for determining the "nodeformation" vertebrae, "wedge-shaped" vertebrae, "inverse wedge-shaped"vertebrae, "fish" vertebrae, and "flat" vertebrae; (iv) measuring a, c,and d from a profile X-ray image of said vertebral body to be judged,storing the measurements in said memory, and determining c/d, a/c, anda/d; and (v) classifying deformation of said vertebral body to be judgedfrom the physical vertebral body measurements c/d in the case of"wedge-shaped", and "inverse wedge-shaped" vertebrae, from c, d, σ_(c),σ_(d), and c/d in the case of "flat" vertebrae, and from c, d, σ_(c),σ_(d), a/c, a/d, and c/d in the case of the "no deformation" and "fish"vertebrae, in order to diagnose deformation and to monitor the effect oftherapy on said vertebral body to be judged; wherein said step (v) iscarried out according to the following sub-steps: (i) c/d≧β₁ . . .wedge-shaped vertebrae (or anterior wedge fracture) (ii) c/d≦β₂ . . .inverse wedge-shaped vertebrae (or inverse anterior wedge fracture)(iii) c<c-β₃ σ_(c), d<d-β₄ σ_(d), and β₂ <c/d<β₁ . . . vertebrae (orcompression fracture) (iv) β₂ <c/d<β₁, a/c≦β₅, a/d≦β₆ and, c≧d-β₃ σ_(c)and/or d≧d-β₄ σ_(d) . . . fish vertebrae (or central biconcave fracture)(v) β₂ <c/d<β₁, c≧c-β₃ σ_(c) and/or d≧d-β₄ σ_(d), and a/c>β₅ and/ora/d>β₆ . . . No deformation (or no fracture), wherein β₁ to β₆ areselected as follows: 1.25≦β₁ ≦1.55, 0.6≦β₂ ≦0.8, 1≦β₃ ≦2.5, 1≦β₄ ≦2.5,0.65≦β₅ ≦0.9, and 0.65≦β₆ ≦0.9; and wherein β₁ to β₆ are 1.33≦β₁ ≦1.5,0.65≦β₂ ≦0.75, 1.25≦β₃ ≦2.25, 1.25≦β₄ ≦2.25, 0.7≦β₅ ≦0.85, and 0.7≦β₆≦0.85.